Excess relative risk as an effect measure in case-control studies of rare diseases

Epidemiologists often use ratio-type indices (rate ratio, risk ratio and odds ratio) to quantify the association between exposure and disease. By comparison, less attention has been paid to effect measures on a difference scale (excess rate or excess risk). The excess relative risk (ERR) used primarily by radiation epidemiologists is of peculiar interest here, in that it involves both difference and ratio operations. The ERR index (but not the difference-type indices) is estimable in case-control studies. Using the theory of sufficient component cause model, the author shows that when there is no mechanistic interaction (no synergism in the sufficient cause sense) between the exposure under study and the stratifying variable, the ERR index (but not the ratio-type indices) in a rare-disease case-control setting should remain constant across strata and can therefore be regarded as a common effect parameter. By exploiting this homogeneity property, the related attributable fraction indices can also be estimated with greater precision. The author demonstrates the methodology (SAS codes provided) using a case-control dataset, and shows that ERR preserves the logical properties of the ratio-type indices. In light of the many desirable properties of the ERR index, the author advocates its use as an effect measure in case-control studies of rare diseases.